This reminds me of a time on one of the Celebrity ships when a couple sat down next to us on the starboard side of the pool deck. He lit up a cigar, and I politely told him that smoking was on the port side. He said, "This IS the port side. We docked with this side of the ship at the port". Obviously a first time cruiser!

Barbados--starboard side likely to face land across the harbor, port side to face the dock and sea beyond
St. Thomas--starboard side to face dock, BUT port side has better view ocross the harbor to the town of Charlotte Amalie!
Antigua--bow points straight into land (pier juts straight out into the harbor)

On CP Western Caribbean, we had tender for Princess Cays & Grand Cayman.

For Monetgo Bay, we docked starboard side.
For Cozumel, we docked port side (could have very well had been starboard).

At Cozumel, there are 2 piers cruise ships can dock - one's further away from the main shopping mall while the other is directly across the street from it. We got lucky and were allocated the closer pier. The pier can accomadate 2 ships and it did for the two days - Carnival had the Sensation & Paradise docked starboard side, across the pier from us.

Having been on 25 cruises, worked on ships for 50 years and have contracts with major tanker companies, 80% of the time the ship will tie up starboard side to the dock or pier. Ships very rarely tie up with bow in. Hopes this helps